Theoretical Perspectives on
Transfers and the Role of NTA
Ronald Lee
UC Berkeley
Jan 19, 2006
Thanks to Gretchen Donehower, Tim Miller, Andy
Mason and Paul Lau.
Goal of this talk
• overview of how transfers fit into various
economic theories
• Explain relevance of NTA
• Will not give much detail.
Outline of talk
• Overview of transfers and theory
• Fertility, altruism, HK and transfers
– Altruism and bequests
• Population and Economic Growth
– Optimal paths
– Population change, life cycle saving and economic
growth
– Comparative simulations over demographic transition
Transfers are central to theories of
both fertility and economic growth
• Capital intensity of economy depends on
willingness of population to hold capital rather
than spending it for current gratification.
• Motivations to hold capital include
– Life cycle consumption smoothing (yl(x), c(x))
– Desire to make transfers to next generation, inter
vivos or end of life (bequests, other downward
transfers).
– But expected transfers for old age substitute for K.
• Planned total transfer per child is the (shadow)
price of a child to a parent.
Theory also bears on form of
transfers
• Transfer as cash (K) or HK?
– Invest in HK of child until its rate of return equals rate
of return on K (this is optimal amount of HK).
– Give balance of desired transfer amount as K if
positive.
• If desired transfer amount is less than the
optimal investment in HK, then
– Investment in child is inefficiently low, or
– Parent seeks to ensure repayment of part of full cost
of optimal HK investment.
Theory also bears on public-private
interaction
• Becker-Murphy etc:
– Govt may introduce public education in
response to parental under-investment in
education
– Parents are compensated for cost in excess
of their desired transfer amount by introducing
a public pension program.
Efficacy of public intergenerational
redistribution depends on private
motivations
• Motivation: altruism or exchange?
– Real transfers are motivated by altruism in our use of
the word “transfers”
– Apparent transfers may actually be exchanges within
the family: loans and their repayment, money for
services, etc.
• Altruistically motivated private transfers will be
used to undo the effects of public transfer
programs, provided parents wish to make
positive bequests to their children before the
public program.
Efficacy (cont.)
• Barro: If parents were already giving bequests or
other transfers, then they will increase their
transfers to their kids to undo the effects of the
public pension.
• If parents do not wish to make positive bequests
then public policies will be effective.
– If apparent transfers are really exchanges then
parents do not want to make bequests.
• There is a growing empirical literature on
altruism versus exchange.
Those are general theoretical
ideas; now more detail
• NTA includes countries at different levels
of development, different public sector
programs, different levels of mortality etc.
• NTA will include changes over time within
countries.
• These theories often predict what
observable changes will occur as income
rises, as public sector programs become
more important etc.
Basic altruistic fertility theory with
bequests
• “bequests” B here means all
transfers to children.
• Utility of parents depends on
own life time cons, children’s
av life time cons, and number
of kids.
• They decide how much to
bequeath to child, B. For now,
take n as given.
• Bequest is larger if:
– They are more altruistic
– Their wage is higher
– Their kid’s wage will be lower.
max ct ,ct 1 ut  ct , nt , ct 1 
s.t. ct  wt  nt B
ct 1  1  r  B  wt 1
Now consider human capital
• Parents can either invest in education, e,
or leave a cash bequest, b, where B=b+e.
• Earnings of child as adult are: g(e)wt+1.
• Income of child as adult is:
(1+r)b + g(e)wt+1
• Optimal parental plan is invest in
education up to e* where its marginal
product = r:
r = g′(e*)wt+1
How does e* compare to B?
• If e* less than B, the intended total bequest or
transfer, then parents simple leave a cash
bequest b = B-e* of the difference. No problem.
• If e* greater than B then things get interesting.
– Parents make loans to children for e*-B, and children
repay them with old age support if repayment can be
assured.
– If repayment cannot be assured, then investment in
education is too low (e<e*), income remains low, and
fertility remains high. More later.
What is B? Public and private
components of “bequests” in NTA
• Costs of rearing, other consumption (OC) (Exclude from
B?):
– Parental transfer for other consumption (OC).
– Public welfare for kids in poor families
• Investment in HK (HK) public and private:
– Education
– Health
• Inter vivos transfers to adult children (AIV)
• End of life bequests, public and private (EOL)
– Public: National debt, public infrastructure and other capital,
natural resources (not yet included)
– Private: end of life bequests
More on estimating B
• B is the sum of pub and priv downward transfers
per child,
B = OC + HK + AIV + EOL
• This is a longitudinal net present value at birth
measure, which might be constructed from the
cross-sectional accounts under appropriate
assumptions.
• Eventually perhaps it can be calculated
longitudinally as we did for the main public
transfers in the US and in France
B in the US for generation born in
2000 (rough, many assumps)
• Use cross-section for 2000.
• Assume transfers rise at 1.5% per year
(prod gr)
• Discount at 3%
• Adjust public transfers for future budget
balance (50-50 cut taxes, cut benefits)
• Assume public debt = public capital
Value of B for US newborns in 2000
(NPV at birth)
• NPV of Public Transfers (Pub Ed, Soc Sec
and Medicare only) assuming budget is
balanced 50-50 by cutting taxes and
benefits:
+47K
(assumes govt debt = value of pub capital)
• NPV of Intervivos familial transfers
received including consumption: 220K
• Private end of life bequests:
27K
• Total: 294K
B in context
• Relative to NPV of child’s life time
earnings = 34%
• Health and Education as a share of total
bequest = 33%
• Private as a share of B = 84%
Some questions for future work
• How has B changed over 20th Cent?
– Has it fallen with rise of transfers to elderly in
second half of century?
– Private transfers have surely fluctuated along
with fertility, lower for baby boom gens, higher
after.
• Compare similar calculations across
countries.
P is sum of gross upward transfers to adults,
mainly to elderly (double counting with B, so
caution needed)
• Components of P
– Familial transfers to elderly
– Public transfers including
Hypotheses about these components of
B and P per individual cross nationally
• Basic idea:
– Altruism sets size of total B, P.
– Private takes public as given and makes up
the target total.
• HK spending per child is positively
associated with income and negatively
with fertility.
• Here is a rough and preliminary look at six
countries.
Total Spending on Education and Health
Care for Children by TFR in Preceding
Years, Selected Countries
6
5
Ratio of Tot Spnd to Av Lab Inc 30-49
Relative to
labor
income age
30-49
4
3
2
1
0
0
0.5
1
1.5
2
TFR in preceding five years
2.5
3
3.5
• For given income and fertility
– public and private HK expenditures per child
are negatively correlated.
– Public and private P are negatively correlated.
• Public pensions and elder co-residence with adult
children are negatively related (but kids may coreside with parents who receive pensions)
– Public P and private transfers to adult children
(AIV + EOL) are positively related. (Barro
idea: private undoes public)
Hypotheses (cont.)
• Private AIV and Public transfers per child are
positively correlated with income and negatively
with fertility.
• Holding income and fertility constant
– K (capital per capita) is positively associated with B.
(e.g. Kotlikoff-Summers: bequest motive accounts for
most K)
– K (capital per capita) is negatively associated with P.
(e.g. Feldstein: pub PAYGO pensions displace capital;
here also familial transfers)
– National saving rates are negatively associated with
P, other things equal. (Flow version of K argument).
Empirical questions for a single
country
• What is the sign of B? What is its size relative to
per capita income or labor inc 30-49 or life time
earnings?
• How has it changed historically?
• What are the shares of public and private
components of B?
– What are the relative public and private shares of OC,
HK, AIV and EOL?
• How does B vary across countries? Is it related
to income? Fertility? How about HK alone?
Fertility, altruism, HK and transfers
(a la Willis, 1987)
• Think of three stages of economic
development
– 1. Poor, very low returns to human capital
– 2. Technical Progress and declining mortality
raises returns to HK and incomes
– 3. Continuing tech progress means high rates
of return to HK and incomes
• Now consider implications for fertility and
transfers
1. Poor and low returns to HK
means
• B is low relative to income (low shadow
price)
• Consequently fertility is high
• Child labor
• Relatively large material bequests to
children, e.g. dowries, farms
• Minimal old age support
2. Medium, returns to HK have
started to rise
• With higher returns to HK and higher income,
parents choose higher B (higher shadow price)
• Fertility falls
• Optimal HK exceeds desired B, then parents
make familial loans to children (if repayment is
assured)
• These are repaid as Old Age Support, which in
NTA appear to be transfers for OAS but are in
fact exchange.
• parents make implicit loan to children to get to
optimal investment in HK.
But if institutions do not support
repayment of HK loans, then
• inability to enforce negative bequests
(repayment of implicit loans) means there
is too little investment in education.
• In this case, public education may lead to
efficient investment in education.
• If followed by public pensions (repayment
of parents) then this could be Pareto
improvement (see Becker and Murphy)
3. High income, low mortality, and
very high returns to HK.
• B grows to exceed optimal HK so parents
want to make additional transfers to
children
– so familial support of the elderly declines
– Elderly do life cycle saving and/or receive
public pensions.
– parents start to make private transfers to their
children at every life cycle stage.
– Children very costly so fertility very low
Population and Economic Growth
• Consider the demographic transition and
population aging
• How can NTA measures and concepts
help?
• Accounting measures describe what is but
don’t tell us what might be if something
changes – that requires theory,
assumptions.
Alternative Approaches
• How is the optimal outcome affected by
population change and life cycle measures?
• How does population change affect the economy
given a rule of individual behavior (life cycle
saving)?
• If existing patterns of transfers and asset
accumulation remain similar, how will the
economy be affected by population change?
• In all cases ignore effects of scale and natural
resources; focus on age distribution and growth
rates.
Concepts
• For given life time c(x)
and yl(x), life cycle wealth
W(x) is the wealth a
generation would need to
hold at age x to achieve
  rx
the consumption path c(x) W  x   x e l  a  c  a   yl  a  da
for given earnings path
yl(x), per original member
• Assumes generational
sharing of mortality risk.
• I have suppressed t, but
this is a longitudinal
concept.
Aggregate life cycle wealth
• Aggregate life cycle
wealth W is the
population weighted
average of W(x).
• N(x) is the proportion of
the population at age x,
so W is life cycle wealth
per capita in the
population.
• It is a cross-sectional
weighted average of the
longitudinal W(x) values.

W   N ( x)W ( x)dx
0
Transfer wealth
• T(x) is transfer wealth at age x
• It is the survival weighted present value of
expected future transfers received minus
future transfers made to others.
• T is the population weighted sum
analogous to W, expressed as per capita
average.
Capital
• K(x) is holding of capital at age x.
• K is per capita figure.
• W(x) = T(x) + K(x)
– Life cycle wealth can be held either as K or as
expected net transfers in the future. Credit is another
possibility I ignore here for simplicity.
• Aggregate identity: W= T + K
• Positive transfer wealth substitutes for K in
satisfying demand for life cycle wealth.
• Or let B# = -T be Aggregate Bequest Wealth
• K = W + B# = W+(-T), and the demand for capital
is the demand for life cycle wealth plus the
demand for bequest wealth.
Figure 1. The demand for K by producers, the demand for life cycle
wealth W, and transfer wealth T (all measured at population level on
per capita basis)
K(r,n)=demand for
capital by producers
r>n
r=n
Wealth, capital
After Willis (1988); Lee (1994)
W(r,n)= life cycle wealth
Figure 1. The demand for K by producers, the demand for life cycle
wealth W, and transfer wealth T (all measured at population level on
per capita basis)
K(r,n)=demand for
capital by producers
W(r,n)= life cycle wealth
T=0; pure life cycle saving.
saving
Demand for K is just for
consumption smoothing over
life cycle.
r>n
r=n
Modigliani’s Dream
Wealth, capital
After Willis (1988); Lee (1994)
Figure 1. The demand for K by producers, the demand for life cycle
wealth W, and transfer wealth T (all measured at population level on
per capita basis)
K(r,n)=demand for
capital by producers
T>0
T>0; life cycle demand for wealth
partly satisfied by PAYGO pensions
or by familial transfers to elderly.
Less K and higher r than in pure life
cycle saving case.
r>n
r=n
W(r,n)= life cycle wealth
Golden Rule
Feldstein’s Nightmare
Wealth, capital
After Willis (1988); Lee (1994)
Figure 1. The demand for K by producers, the demand for life cycle
wealth W, and transfer wealth T (all measured at population level on
per capita basis)
K(r,n)=demand for
capital by producers
r>n
r=n
Golden Rule
W(r,n)= life cycle wealth
T<0: bequest motive
supplements life cycle
demand for wealth. Total
demand for K exceeds life
cycle demand. K higher, r
lower = n.
Any more K than this would
be inefficient.
T(r,n)= transfer wealth<0
Wealth, capital
After Willis (1988); Lee (1994)
Bequests or govt budget
surplus
Kotlikoff and Summers
Consider optimal paths
• Simplest case: Maximize steady state per
capita consumption: Golden Rule.
• This case shows clearly the role of
transfers and transfer wealth, T.
Population aging and golden rule
steady states
• Population aging is mostly due to low population
growth rates stemming from low fertility, rather
than due to long life.
• Consider the effect of population aging across
golden rule steady states (g.r.s.s.)
• dc/dn=-k
• That is, a decline of .01 in n would lead to an
increase in c by .01*k.
• Slower pop gr and pog aging always raise
per capita consumption across g.r. steady
states.
II. Golden rule steady states with
age structure: basic ideas
• Now let the population have a steady state age
structure e-nxl(x), and let steady state
consumption and earnings by age be c(x) and
yl(x).
• In golden rule, the rate of return on capital and
the discount rate equal n, the pop gr rate.
• Let C = the present value of life time
consumption discounted at rate n and survival
weighted.
  nx
C   e l  x  c  x  dx
0
NTA consumption
age profile
Golden rule steady states with age
structure (2): An Elegant Result
• This result is due to
Arthur and McNicoll
• The effect of a small
variation in n on C is
found by differentiating
across golden rule steady
states, and is:
• The effect on
consumption depends on
the balance of the capital
dilution effect and an
intergenerational transfer
effect (actually, all
reallocations combined)
d ln  C 
dn
k
 Ac  Ayl 
c
NTA average ages of
consumption and
earning.
Golden rule steady states with age
structure (2): An Elegant Result
Proportional change in life time
• This result is due to
consumption when n changes.
Arthur and McNicoll
• The effect of a small
d ln C
k
variation in n on C is

A

A

c
y
l
found by differentiating
dn
c
across golden rule steady
states, and is:
• The effect on
consumption depends on
the balance of the capital
NTA average ages of
dilution effect and an
consumption and
intergenerational transfer
earning.
effect (actually, all
reallocations combined)
 
Interpretation (cont.)
• After manipulation, the expression
k
Ac  Ayl 
c
can be seen to equal simply T/c, the ratio of transfer
wealth to per capita consumption.
In other words, the effect of more rapid or less rapid
population growth, across golden rule steady states,
depends only on the ratio of transfer wealth, in family
and public systems, to per capita consumption.
This quantity is readily calculated from NTA measures.
With age we get a different picture
• Define life time consumption C=P.V. of survivalweighted life time consumption, c(x).
• Striking result: dln(C)/dn = T/c
• Life cycle consumption either rises or falls
depending on whether the T necessary to
achieve r=n is positive or negative.
• In case shown in diagram T<0 for golden rule,
so slower pop growth and pop aging raise C.
Result due to Willis (1988); also see Lee (1994).
A more interesting optimal setup:
Ramsey-Cass-Koopmans model
• Social Planner
maximizes discounted
value of per capita
utility from
consumption.
V t  
– Here utility is not
weighted by
population size; pop gr
is irrelevant if it is.


t
e
s
u c  s  ds
1
c( s )
u c  s   
1
Can be decentralized to planning by
dynastic families a la Becker-Barro
• Then don’t need social planner
• Discounting is per generation.
• Future generations also get weighted in a
flexible way by their size, allowing for
weights proportional to size, or for no
weighting by size (per capita utility
criterion), or intermediate cases.
• Will not pursue here; for future.
Other assumptions made here
• c(s) is aggregate consumption per equivalent adult
consumer net of tech prog,
that is times e-g(s-t)
• Cobb Douglas production
• Parameter values:
g=.015
tech progress
ρ=.01
discount rate (degree of altruism)
δ=.03
depreciation
Cobb-Douglas coeffs: labor=2/3, cap=1/3
Elasticity of intertemporal sub (theta)=.4
Setup similar to Cutler et al (1990), but some critical diffs, too.
• Perfect demographic foresight by planner.
Now look at optimal trajectories for
three countries
• US, Taiwan (without immig from
Mainland), Niger
• Assume demographic steady state
reached in 2300 (UN projections) and
economic also; can solve this analytically
• Find optimal trajectory from 2006 to 2300
by numerical search.
Support Ratios for US, Niger, and PseudoTaiwan, with own c(x) and yl(x) age profiles
(2000-2150)
1
Ratio of Effective Workers to effective consumers
0.9
Taiwan
Niger
0.8
0.7
0.6
US
US
Niger
Taiwan
0.5
0.4
US has declining support ratio because
cons is very high for old age.
0.3
0.2
Niger shows effect of demographic
transition, demog dividend, then pop aging.
0.1
0
1980
2000
2020
2040
2060
2080
Date
2100
2120
2140
2160
Consumption per Effective Consumer net of tech progress:
Social Planner, 2006-2150
Consumption per Effective Consumer relative to 2006; Social Planner, 2006 to 2150
4
Consumption per Effective Consumer net of technological
progress
Consumption rises in all countries.
3.5
3
2.5
Most in Niger, because it started out with little
capital and rapid pop gr.
Even in US and Taiwan consumption rises
despite population aging.
US
Niger
Taiwan
2
1.5
1
0.5
0
1980
2000
2020
2040
2060
2080
Date
2100
2120
2140
2160
Life Cycle Wealth, Transfer Wealth and Capital in
US, Niger and Taiwan: Social Planner, 2006-2150
Life Cycle Wealth, Transfer Wealth and Capital in Social Planner's US as Ratios to Labor
Income
Life Cycle Wealth, Transfer Wealth and Capital in Social Planner's Taiwan, Ratios to Labor
Income
20.00
K/Yl
20.00
10.00
10.00
2000
2020
2040
2060
2080
2100
2120
2140
W/Yl
2160
-10.00
T/Yl
-20.00
Series1
Series2
Series3
2000
2020
2040
2060
-30.00
2080
2100
2120
2140
2160
-10.00
(W/YL)
(K/YL)
(T/YL)
-20.00
-30.00
US
-40.00
Taiwan
-40.00
-50.00
Date
-50.00
Date
Life Cycle Wealth, Transfer Wealth and Capital in Niger, Ratios to labor income
20.00
Some points to note:
All three end up at same cap intensity.
Life cycle wealth is greater in US due
to high consumption in old age.
Taiwan and Niger both require much
greater downward transfers (bequests)
to achieve optimal capital intensity.
10.00
0.00
1980
Ratio to Labor Income
Ratios to Labor Income
0.00
1980
Ratio to Labor Income
0.00
1980
2000
2020
2040
2060
2080
2100
2120
2140
2160
-10.00
(W/YL)
(K/YL)
(T/YL)
-20.00
Niger
-30.00
-40.00
-50.00
Date
Population change, life cycle
saving and economic growth
• This part does not use NTA estimates, except labor
income over the life cycle.
• Household members supply labor based on yl(x) profiles.
• Unisex household composition by age of head simulated
based on fertility, mortality, and age of kids at leaving
home.
• Household labor income is projected based on expected
productivity growth.
• Consumption is allocated to household members in
proportion to equivalent adult consumer weights.
Life cycle saving (cont.)
• Life time budget constraint for household is P.V.
of survival weighted expected future labor
earnings of all household members.
• Consumption path for household is chosen to
maximize expected utility of household head,
given subjective discount rate and rate of
intertemporal substitution.
• No bequests; no transfers; no public sector.
Open economy, so r and w are given.
Demographic transition has several
effects
• Lower mortality means longer period in
retirement, requires higher saving rate
(behavioral).
• Lower fertility means adults keep greater share
of life time income for own consumption,
including in retirement, so need to save more
(behavioral)
• Older population implies a greater population
share of older adults who hold the most wealth
(capital), and therefore more capital per person
in population (compositional).
Cases simulated
1.
2.
Pure life cycle saving, as just described
Life cycle saving wrapped around familial transfers to
elderly
–
–
3.
Need to save less or nothing for old age
May need to save in anticipation of supporting own parents.
Persistent share of transfers
–
–
–
–
Observed cross-sectional age profile of consumption is
maintained through intergenerational sharing.
shares of old age consumption funded by transfers and by
assets remains fixed as the population ages.
Changing transfers to children as fertility and mortality fall also
taken into account
Determines unique trajectories
Simulated Capital/Income Ratio Under Life Cycle Savings for Taiwan
Demography, 1900 to 2050, Assuming No Familial Transfers to Elderly
6
5
LC Model Results
Ratio
4
3
No Transfers
2
1
0
1900
1950
2000
2050
6
Simulated Capital/Income Ratio Under Life Cycle Savings for Taiwan
Demography, 1900 to 2050, Assuming NTA Style Familial Transfers to
Elderly with Co-Residence
5
LC Model Results
Ratio
4
3
No Transfers
2
1
0
1900
Family Transfers
1950
2000
2050
6
Simulated Capital/Income Ratio Under Persistent
Transfers Model (.35, .65) Compared to Life Cycle
Savings for Taiwan Demography, 1900 to 2050
LC Model Results
Constant Tau Results
5
Ratio
4
3
Tau=0.35
No Transfers
2
1
0
1900
Tau=0.65
Family Transfers
1950
2000
2050
6
5
Simulated Capital/Income Ratio Under Fixed Tau Model (.35, .65)
Compared to Life Cycle Savings for Taiwan Demography, 1900 to
2050, and showing Actual Capital/Income Ratio and Wealth/Income
Ratio
LC Model Results
Constant Tau Results
Actual Capital/Income Ratio
Actual Wealth/Income Ratio
4
Ratio
Tau=0.35
3
No Transfers
2
1
Tau=0.65
Family Transfers
0
1900
1950
2000
2050
6
Figure 1. Simulated Capital/Income Ratio Under Fixed Tau Model (.35, .65)
Compared to Life Cycle Savings for Taiwan Demography, 1900 to 2050, and
showing Actual Capital/Income Ratio and Wealth/Income Ratio
LC Model Results
5
Social Planner
Constant Tau Results
Actual Capital/Income Ratio
Actual Wealth/Income Ratio
4
Ratio
Tau=0.35
3
No Transfers
2
1
Tau=0.65
Family Transfers
0
1900
1950
2000
2050
All four show major capital deepening following fertility decline and pop
aging.
Timing is several decades earlier in the Persistent Transfers model.
6
Figure 1. Simulated Capital/Income Ratio Under Fixed Tau Model (.35, .65)
Compared to Life Cycle Savings for Taiwan Demography, 1900 to 2050, and
showing Actual Capital/Income Ratio and Wealth/Income Ratio
LC Model Results
5
Social Planner
Constant Tau Results
Actual Capital/Income Ratio
Actual Wealth/Income Ratio
4
Ratio
Tau=0.35
3
No Transfers
2
1
Tau=0.65
Family Transfers
0
1900
1950
2000
2050
Simulated Saving Rate Under Life Cycle Savings for Taiwan
Demography, 1900 to 2050, Assuming No Familial Transfers to Elderly
30
No Transfers
25
LC Model Results
Percentage
20
15
10
5
0
1900
-5
1950
2000
2050
30
Simulated Savings Rate Under Life Cycle Savings for Taiwan
Demography, 1900 to 2050, with NTA Style Transfers to Elderly and
Coresidence
No Transfers
25
LC Model Results
Percentage
20
Family
Transfers
15
10
5
0
1900
-5
1950
2000
2050
Simulated Savings Rate Under Fixed Tau Model (.35, .65) Compared
to Life Cycle Savings for Taiwan Demography, 1900 to 2050
30
No Transfers
25
LC Model Results
Constant Tau Results
Percentage
20
Family
Transfers
15
10
Tau=0.35
5
Tau=0.65
0
1900
-5
1950
2000
2050
Simulated Savings Rate Under Fixed Tau Model (.35, .65) Compared
to Life Cycle Savings for Taiwan Demography, 1900 to 2050
30
25
LC Model Results
Constant Tau Results
Actual Net Private Savings Rate
Actual Household Savings Rate
Percentage
20
No Transfers
Family
Transfers
15
10
Tau=0.35
5
Tau=0.65
0
1900
-5
1950
2000
2050
Figure 2. Simulated Savings Rate Under Fixed Tau Model (.35, .65)
Compared to Life Cycle Savings for Taiwan Demography, 1900 to
2050
Social Planner
30
25
LC Model Results
Constant Tau Results
Actual Net Private Savings Rate
Actual Household Savings Rate
Percentage
20
No Transfers
Family
Transfers
15
10
Tau=0.35
5
Tau=0.65
0
1900
-5
1950
2000
2050
Saving rates rise following fertility and mortality decline in all approaches, but
earliest in the Persistent Transfer approach. Only under Social Planner do they
stay high with population aging.
Figure 2. Simulated Savings Rate Under Fixed Tau Model (.35, .65)
Compared to Life Cycle Savings for Taiwan Demography, 1900 to
2050
Social Planner
30
25
LC Model Results
Constant Tau Results
Actual Net Private Savings Rate
Actual Household Savings Rate
Percentage
20
No Transfers
Family
Transfers
15
10
Tau=0.35
5
Tau=0.65
0
1900
-5
1950
2000
2050
Conclusion
• Transfers are central to theory about fertility,
investment in human capital, investment in
physical capital, economic growth, and the
efficacy of public policies targeted to age groups.
• Theories provide many insights, but can become
sterile if divorced from observation.
• NTA can provide valuable information about
relevant transfers and processes, deepening our
understanding in a number of areas.